Semi-empirical calculations for the ranges of fast ions in silicon

A semi-empirical method is proposed to calculate the ion ranges in energy region E?=?0.025–10?MeV/nucleon. The dependence of ion ranges on the projectile nuclear charge, mass and velocity is analysed. The calculations presented for ranges of ions with nuclear charges Z?=?2–10 in silicon are compared with SRIM results and experimental data.     

Random Measures and Applications

Abstract

A mapping Z(·) from a δ-ring ?₀(?) into the vector space of random variables L ^p (P) is a vector-valued measure if it is σ-additive in the metric of its range. It is a vector measure if the range is a Banach space and a random measure if also its values are independent on disjoint sets. An important reason for this study is to construct integrals relative to such Zs, which typically do not have finite variation. For this, it is essential to find a controlling (σ-finite) measure for Z that is not available if 0 <p < 1, and here the random measure is taken to be p-stable and utilize properties of infinitely divisible distributions. In the case of p = 2, Z(·) induces a bimeasure, and if p > 2 is an integer it induces a polymeasure, either of which need not be (signed) measures on product spaces. Important applications lead to all these possibilities. In all those cases, a detailed analysis of vector-valued set functions is presented, with special focus for the cases of 0 <p < 1 and p = 2 where probability and Bochner's L ^{2, 2} boundedness plays a key role. Specialization if Z is stationary, harmonizable, and/or isotropic are discussed using the group structure of ? ⁿ , n ≥ 1, extending it for an lca group G. If Z is Banach valued or a quasi-martingale measure, methods of obtaining integrals are outlined in the last section, and open problems motivated by applications are pointed out at various places.     

Parallelepipeds and Decomposition of Ranges of Vector Measures in Banach Spaces

We extend a result of A. Neyman about zonoids in ℝⁿ to zonoids in Banach spaces. A zonoid in a Banach space is the closed convex hull of the range of a vector measure. We show that the following conditions on a zonoid Z are equivalent: (1) Z determines univocally the associated conical measure; (2) There exists a vector measure defined on (Ω, Σ) such that every decomposition of Z into sum of zonoids can be obtained by decomposing (Ω, Σ); (3) Z ∩ (—αZ) is a parallelepiped for every α > 0. We also prove other results about decomposition of zonoids; for instance, we prove that if Z is a zonoid and Z ∩ (—Z) is a zonotope, there exists a zonoid L such that Z = Z ∩ (—Z) + L.     

Radiation enhanced diffusion in face centered cubic cu-zn alloys

The enhancement of diffusion by neutron irradiation has been investigated on a Cu-36 percent Zn alloy for various neutron fluxes and irradiation temperatures by means of in-pile measurements of electrical resistivity. For fresh samples the diffusion rate depends on temperature with an activation energy of 0.35 eV. During repeated irradiations the diffusion rate decreases and becomes nearly temperature independent. The variation of the concentration of interstitials and vacancies with irradiation time has been numerically calculated for various neutron fluxes, irradiation temperatures and sink concentrations. A comparison of the experimental and theoretical results shows that the point defects annihilate in fresh samples mainly by pair recombination and in samples which had been repeatedly cycled by pair recombination and at fixed sinks. Point defect clusters acting as sinks are created during the course of the irradiation as shown by electron microscope investigations. The radiation enhanced diffusion rate was found to depend on interstitials only, the activation energy of which was determined to 0.70 eV.     

Ranges and profiles of distribution of low-energy ions channeling in metal and semiconductor single crystals

In the present work peculiarities of trajectories and energy losses, ranges and profiles of distribution of low-energy different-mass ions channeling in thin single crystals of metals and semiconductors have been thoroughly studied by computer simulation in binary collision approximation. The character of oscillations of channeled-ion trajectories depending on their energies, aiming points from the axis of a channel, kind of interaction potential, crystal lattice type and temperature has been determined. It has been found that, in the case of light ions even at low energy, the main contribution to energy loss is made by inelastic energy losses, whereas for heavy ions, already at E < 10 keV, elastic energy losses exceed inelastic ones. Profiles of the distribution of channeled ions have been calculated depending on crystal lattice type, kind of ions and their energy.